Information about the side of the mirror (left or right) while using mirror modifier?
you can select one part of the mesh by using a two-tone texture with halves along the axis, in this texture the x axis have the red tone, meanwhile the y axis have the green tone, in this way you can either select texture U ,V or both that provides the mirror modifier.



In material you put the above texture in the red node, in node green you use the node group setup of the second panel, and you must place the UV "mesh" in only one halve. With this node-setup you have the information of U texture or V texture, and you could also work with symmetrical or asymmetrical textures, like the example, in the blue node you have a symmetrical texture, meanwhile in the yellow node you have an asymmetrical texture.

UPDATE

Apparently there's no need for an auxiliary texture, the blend file with the groupnode is here http://pasteall.org/blend/index.php?id=46015, set 0-1 for bypassing the symmetrization of the UV coordinates, set 1-2 for U texture, set 2-3 for V texture, set 3-4 for U and V texture symmetrization. The node also gives you the mask of each coordinate.